Rewrite as a simplified fraction. ${1.4\overline{57} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 1457.5757...\\ 10x &= 14.5757...\end{align*}}$ Subtracting the two equations, we have: ${990x = 1443}$ ${x = \dfrac{1443}{990}} $ ${x = \dfrac{481}{330}} \text{or} {1 \dfrac{151}{330}}$